Rewrite as a simplified fraction. ${2.\overline{2} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 22.2222...\\ 1x &= 2.2222...\end{align*}}$ Subtracting the two equations, we have: ${9x = 20}$ ${x = \dfrac{20}{9}} \text{or} {2 \dfrac{2}{9}}$